Question

Find the reciprocal of each of the following fractions. Classify the reciprocal as a proper fraction, improper and whole number.
\[\dfrac{1}{{11}}\]

Answer 1

Hint: Let us find the numerator and denominator of the reciprocal of the given number and then compare that to find whether the reciprocal is proper fraction, improper fraction or whole number.

Complete step-by-step answer:
As we know that if \[\dfrac{{\text{a}}}{{\text{b}}}\] is a fraction number then numerator of \[\dfrac{{\text{a}}}{{\text{b}}}\] will be a and denominator of \[\dfrac{{\text{a}}}{{\text{b}}}\] will be b.
As we know that if \[\dfrac{{\text{a}}}{{\text{b}}}\] is any fraction number that if we are asked to find the reciprocal of it. Then we replace numerator with denominator and denominator with numerator. And the resultant number \[\left( {\dfrac{{\text{b}}}{{\text{a}}}} \right)\] will be the reciprocal of \[\dfrac{{\text{a}}}{{\text{b}}}\].
So, the reciprocal of the given number \[\dfrac{1}{{11}}\] will be \[\dfrac{{11}}{1} = 11\].
As we know that if the numerator of any fractional number is greater than the denominator of that fractional number, then the number will be an Improper fraction.
If the numerator of any fractional number is lesser than the denominator of that fractional number, then the number will be a proper fraction.
And if the denominator of the fractional number is 1 then the number will be the whole number.
So, now we can see that the denominator of the reciprocal of the given number is 1. So, the reciprocal of the given number will be the whole number.
Hence, the reciprocal of \[\dfrac{1}{{11}}\] is 11 and it is the whole number.

Note: Whenever we come up with this type of problem then first, we find the reciprocal of the given number by interchanging denominator and numerator, and after that to find which type of fractional number it is, we compare the numerator with the denominator. If denominator is equal to 1 then the number will be whole number, if numerator is less than denominator then number will be proper fraction otherwise number will be improper fraction.